64 DISPLACEMENT INTERFEROMETRY BY 



& 

 contractions were again remarkably consistent. Consecutive mean results 



for instance are : 



io 5 A./V/AP=i52 156 153 135 132 137 168 168 152 147 cm. 



10~ 11 E= 2-5 2-4 2-5 2.8 2.8 2-7 2.2 2.2 2-5 2.6 



As the rods were drawn and not ground true and fitted the sleeve loosely, 

 the occurrence of some dislocation in the data obtained in the three different 

 series is perhaps inevitable. Again the maximum difference of AN is within 

 4X icr 4 cm. and with a micromter reading to io~ 4 cm. some of this is observa- 

 tional error. The results, however, show conclusively that even when the 

 glass rod is apparently thin enough as compared with its length, the actual 

 value of the modulus is not obtained. Some outstanding discrepancy has 

 escaped detection. 



34. Same. Steel. A final test of the degree of insufficiency of the appa- 

 ratus was made by using steel rods loosely fitting the original sheath. Their 

 dimensions were: 



= g.2 cm. 2r = o.37 cm. = 



Such rods are, of course, far too rigid and thick for the apparatus and the 

 displacement per kilogram would be but 



less than the mean wave-length of light, while the micrometer registers but 

 icr 4 cm. It would be necessary, therefore, to work with fringes in any 

 case, even if the apparatus were sufficiently rigid, etc., to guarantee such 

 small displacements. In the best results from triplets between 3 and 4 kg., 

 io 5 A./V/AP = 22 cm., equivalent to icr 12 = 0.4, could not be improved, and 

 yet this is about 5 times too small. Steel rods less than a millimeter thick 

 would have to be used if a trustworthy value of E were aimed at. 



35. Modifications of apparatus. The above apparatus failed in case of 

 rods of high rigidity and insufficiently reduced sectional areas. Brass and 

 steel rods 2 cm. long will have to be at least as thin as i mm. in diameter 

 if the data for E are to be trustworthy. There is, in other words, a source of 

 error in the apparatus itself, by which AJV/AP is incremented; and this is 

 to be sought in the method by which stresses are applied. Though each rod 

 is supported at one end by the friction at its contact with the abutment 

 A, figure 28, and at the other by the thread of the bifilar suspension, this 

 support is not guaranteed to the extent required. The vertical bifilar stress 

 yields in its relation to the much larger horizontal stresses of the loads, so 

 that the bar F undergoes independent slight rotations around vertical and 

 horizontal axes of its own. This is evidenced by the fact that the fringes 

 sometimes change their inclination, or the two white slit-images may to a 

 small degree lose their full coincidence (flexure). 



The occurrence of the hysteresis loops in case of hard rubber may be 



